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Convergence of Singular Integral Operators in Weighted Lebesgue Spaces

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Abstract (2. Language): 
In this paper, the pointwise approximation to functions f G L1w (a, b) by the convolution type singular integral operators given in the following form: where (a, b) stands for arbitrary closed, semi closed or open bounded interval in R or R itself, L1w (a, b) denotes the space of all measurable but non-integrable functions f for which f is integrable on (a, b) and w : R — R+ is a corresponding weight function, at a ^-generalized Lebesgue point and the rate of convergence at this point are studied.
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